Most nuclei are deformed, and these deformations play an important role in various nuclear and astrophysical phenomena. Microscopic nuclear-mass models have been developed based on covariant density-functional theory to explore exotic nuclear properties. Among these, we adopt mass models based on the relativistic continuum Hartree-Bogoliubov theory (RCHB) with spherical symmetry and the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with axial symmetry to study the effects of deformation on the abundances produced during the rapid neutron-capture process ($r$ process). Since the DRHBc mass table has so far been completed only for even-$Z$ nuclei, we first investigate whether a deep neural network (DNN) can be used to extend the DRHBc mass table by focusing on nuclear binding energies. To incorporate information about odd-odd and odd-even isotopes into the DNN, we also use binding energies from AME2020 as a training set, in addition to those from the DRHBc mass table for even-$Z$ nuclei. After generating an improved mass table through the DNN study, we conduct a sensitivity analysis of $r$-process abundances to deformation or mass variations using the ${\mathrm{RCHB}}^{★}$ and ${\mathrm{DRHBc}}^{★}$ mass tables, where $★$ indicates that the mass table is obtained from the DNN study. For the $r$-process sensitivity study, we consider magnetohydrodynamic jets, collapsar jets, and neutron-star mergers. Our findings indicate that $r$-process abundances can be sensitive to nuclear deformation, particularly within the mass range of $A=80–120$.

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• Binding energy & masses
• Nucleosynthesis in explosive environments
• Bayesian methods
• Deep learning
• Machine learning